You can use deep networks to get better resolution there though, keyword is spectral reassignment, normal methods use maximum likelihood.

What you will get is a variant spectrogram. Method is related to edge directed interpolation and bilateral transform. (You can do the same with log-cepstrum.)

I find this whole exercise linked an undergrad level toy, even in such basic thing as pitch.

The real problem is polyphony and instrument segmentation which this does not begin to touch.